Operator-valued semicircular elements: Solving a quadratic matrix equation with positivity constraints

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We show that the quadratic matrix equation $VW + η(W)W = I$, for given $V$ with positive real part and given analytic mapping $η$ with some positivity preserving properties, has exactly one solution $W$ with positive real part. We point out the relevance of this result in the context of operator-valued free probability theory and for the determination of the asymptotic eigenvalue distribution of band or block random matrices. We also address the problem of a numerical determination of the solution.
14 pages, 2 figures

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Operator Algebras, Complex Variables

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http://salesiana.dossiersoluciones.com/handle/123456789/125926

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703510
 http://arxiv.org/abs/math/0703510

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arXiv